What is an angle with a degree measure of exactly 360 degrees called?

An angle that measures exactly 360 degrees is referred to as a complete angle. This terminology arises from the fact that a complete angle represents a full rotation around a point, returning to the starting position. Consequently, it encompasses the entire circle, as there are 360 degrees in total in one full rotation.

The terminology used in the other options, while they may suggest a similar concept, is not the standard term for a 360-degree angle. "Full angle" and "revolution angle" might imply a similar idea of a complete turn, but they are not the recognized terms within the mathematical community. "Circling angle" is not a standard term used to describe angles in geometry. Understanding the correct terminology is essential for clear communication in mathematics and geometry, especially in educational settings.